1. Have you tried setting the Header alignment to “Right” in “Appearance > Customize > Layout”?
2. You can do this using the Backgrounds add-on.
First, create a semi transparent (with your desired opacity) 4×4 pixel square in Photoshop, then save it as a PNG (with transparency).
Then, go to the Colors area of the Customizer and remove the content background color.
Next, upload the 4×4 image as the content background image, and make sure it’s set to repeat.
Let me know if that works or not 🙂